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Graph Neural Network Autoencoders for Efficient Quantum Circuit Optimisation

Henri Ahola

Published May 22, 2026• 0 citations
OpenAlex

Abstract

Successfully harnessing the power of present-day quantum computing hardware requires efficient utilisation of the limited available resources. Most notably, in the quantum circuit model for computation, circuit depth is severely limited by noisy equipment. Techniques to optimise and reduce depth are consequently necessary. Various approaches exist, but many suffer from poor scalability in practice. In a search for better techniques, this thesis extends preliminary research efforts to implement a quantum circuit compressor or optimiser that utilises a graph variational autoencoder to manipulate circuits in a computationally more manageable latent space. Such latent spaces aim to capture and compress relevant information into far fewer dimensions. This reduces the computational cost of search space exploration and sidesteps the combinatorial explosion that traditional optimisers typically face. As an intermediate implementation and demonstration of the technique, the work presented in this thesis does not yet optimise circuits; it does, however, successfully compress chosen subsets of quantum circuits into a low-dimensional space with a near-100% perfect reconstruction rate. Further work would extend this to additionally manipulate—and eventually optimise—the compressed circuits.

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Successfully harnessing the power of present-day quantum computing hardware requires efficient utilisation of the limited available resources. Most notably, in the quantum circuit model for computation, circuit depth is severely limited by noisy equipment. Techniques to optimise and reduce depth are consequently necessary. Various approaches exist, but many suffer from poor scalability in practice. In a search for better techniques, this thesis extends preliminary research efforts to implement a quantum circuit compressor or optimiser that utilises a graph variational autoencoder to manipulate circuits in a computationally more manageable latent space. Such latent spaces aim to capture and compress relevant information into far fewer dimensions. This reduces the computational cost of search space exploration and sidesteps the combinatorial explosion that traditional optimisers typically face. As an intermediate implementation and demonstration of the technique, the work presented in this thesis does not yet optimise circuits; it does, however, successfully compress chosen subsets of quantum circuits into a low-dimensional space with a near-100% perfect reconstruction rate. Further work would extend this to additionally manipulate—and eventually optimise—the compressed circuits.
Reinforcement learning (RL) is a promising method for quantum circuit optimisation. However, the state space that has to be explored by an RL agent is extremely large when considering all the possibilities in which a quantum circuit can be transformed through local rewrite operations. This state space explosion slows down the learning of RL-based optimisation strategies. We present for the first time how to use graph neural network (GNN) autoencoders for the optimisation of quantum circuits. We construct directed acyclic graphs from the quantum circuits, encode the graphs and use the encodings to represent RL states. We illustrate our proof of concept implementation on Bernstein-Vazirani circuits and, from preliminary results, we conclude that our autoencoder approach: a) maintains the optimality of the original RL method; b) reduces by 20 \% the size of the table that encodes the learned optimisation strategy. Our method is the first realistic first step towards very large scale RL quantum circuit optimisation.
Quantum circuit transformation aims to optimize circuits for depth, gate count, and compatibility with Noisy Intermediate Scale Quantum (NISQ) devices that suffer from various error sources. Prior methods use combinations of expert-defined rules and Reinforcement Learning (RL). We introduce AltGraph, a novel approach employing generative graph models to generate functionally equivalent quantum circuits using—specifically, Direct Acyclic Graph (DAG) Variational Autoencoder (D-VAE) variants (GRU and GCN) and Deep Generative Model for Graphs (DeepGMG). AltGraph perturbs the latent space to generate quantum circuits optimized for hardware coupling maps, reducing gate count by 37.55% and circuit depth by 37.75% post-transpiling, with 0.0074 Mean Squared Error (MSE) in the density matrix—outperforming state-of-the-art methods by 2.56%.
Graph Neural Networks (GNNs) are effective for analyzing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum Computing (QC) may be used to overcome these problems. For instance, Quantum Graph Neural Networks (QGNNs) have already been implemented in the literature. However, current quantum hardware limits the dimensionality of the datasets that can be encoded. For this reason, previous works simplify graph datasets manually or use small synthetic datasets. This work introduces the Guided Graph Compression (GGC) framework. It uses a graph autoencoder to reduce the size of graphs in terms of number of nodes and node feature dimensionality. The compression is guided towards enhancing the performance of a classification task by coupling the loss functions of the autoencoder and the classifier. The framework is applied to the Jet Tagging task that is relevant at CERN's LHC. It involves classifying jets as being originated from quarks or gluons. It is tested on three different training paradigms. First, a classical GNN is trained using the uncompressed data. Then, graph autoencoders are trained as a separate preprocessing step and used for classical and quantum classifiers. Lastly, the GGC framework is applied to both types of classifiers. Results show that the GGC framework outperforms the other two paradigms. Moreover, the classical and quantum classifiers achieve competitive performance in terms of ROC-AUC score.
As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was proposed as a way for the compression of quantum information to reduce resource requirements. Here, we present a strategy to design quantum autoencoders using evolutionary algorithms for transforming quantum information into lower-dimensional representations. We successfully demonstrate the initial applications of the algorithm for compressing different families of quantum states. In particular, we point out that using a restricted gate set in the algorithm allows for efficient simulation of the generated circuits. This approach opens the possibility of using classical logic to find low representations of quantum data, using fewer computational resources.
In recent years, machine learning and deep learning have driven advances in domains such as image classification, speech recognition, and anomaly detection by leveraging multi-layer neural networks to model complex data. Simultaneously, quantum computing (QC) promises to address classically intractable problems via quantum parallelism, motivating research in quantum machine learning (QML). Among QML techniques, quantum autoencoders show promise for compressing high-dimensional quantum and classical data. However, designing effective quantum circuit architectures for quantum autoencoders remains challenging due to the complexity of selecting gates, arranging circuit layers, and tuning parameters. This paper proposes a neural architecture search (NAS) framework that automates the design of quantum autoencoders using a genetic algorithm (GA). By systematically evolving variational quantum circuit (VQC) configurations, our method seeks to identify high-performing hybrid quantum-classical autoencoders for data reconstruction without becoming trapped in local minima. We demonstrate effectiveness on image datasets, highlighting the potential of quantum autoencoders for efficient feature extraction within a noise-prone, near-term quantum era. Our approach lays a foundation for broader application of genetic algorithms to quantum architecture search, aiming for a robust, automated method that can adapt to varied data and hardware constraints.
Abstract Graph neural networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum computing offers a promising avenue to address these issues and inspires new algorithmic approaches. In particular, quantum GNNs (QGNNs) have been explored in recent literature. However, current quantum hardware limits the dimension of the data that can be effectively encoded. Existing approaches either simplify datasets manually or use artificial graph datasets. This work introduces the guided graph compression (GGC) framework, which uses a graph autoencoder to reduce both the number of nodes and the dimensionality of node features. The compression is guided to enhance the performance of a downstream classification task, which can be applied either with a quantum or a classical classifier. The framework is evaluated on the Jet Tagging task, a classification problem of fundamental importance in high energy physics that involves distinguishing particle jets initiated by quarks from those by gluons. We compare GGC to a model that uses the autoencoder as a preprocessing step and to a baseline classical GNN classifier. Our numerical results demonstrate that GGC outperforms both alternatives, while also facilitating the testing of novel QGNN ansatzes on realistic datasets.